Discriminant of a quadratic equation

The discriminant of a quadratic equation in the form ax² + bx + c = 0 is the value of the expression b² - 4ac.

The value of the discriminant determines if the quadratic equation has real or complex numbers solutions.

Case #1:

The value of the discriminant is bigger than 0: b² - 4ac > 0

If the value of the discriminant is bigger than 0, then the quadratic equation has two real solutions and the graph of the related function has two x-intercepts.

The x-intercepts of f(x) = ax² + bx + c  are the solutions of ax² + bx + c = 0.

The figure below shows what the graph looks like with two x-intercepts.

Case #2:

The value of the discriminant is equal to 0: b² - 4ac = 0

If the value of the discriminant is equal to 0, then the quadratic equation has one real solution and the graph of the related function has one x-intercept.

The x-intercepts of f(x) = ax² + bx + c  are the solutions of ax² + bx + c = 0.

The figure below shows what the graph looks like with one x-intercept.

Case #3:

The value of the discriminant is smaller than 0: b² - 4ac < 0

If the value of the discriminant is smaller than 0, then the quadratic equation has no real solution, but two imaginary solutions instead. The graph of the related function has no x-intercept. 

The figure below shows what the graph looks like with no x-intercept.

Recent Articles

• 
• 
• 

1. How To Find The Factors Of 20: A Simple Way

   Sep 17, 23 09:46 AM

   
   There are many ways to find the factors of 20. A simple way is to...

   Read More

2. The SAT Math Test: How To Be Prepared To Face It And Survive

   Jun 09, 23 12:04 PM

   
   The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

   Read More